An Euler method for computing compressible hovering rotor flows is described. The equations are solved using an upwind finite-volume method in a blade-fixed rotating co-ordinate system, so that hover is a steady problem. Transfinite interpolation, along with a periodic transformation, is used to generate grids for the periodic domain. Computation of these flows to an acceptable accuracy requires fine grids, and a long integration time for the wake to develop, resulting in excessive run times on a single processor. Hence, the method is developed as a multiblock code in a parallel environment, and various aspects of data passing and communication between processors have been considered. It is shown that a considerable increase in performance is available from the use of non-blocking and asynchronous communication. It is also demonstrated that increased performance may be available by balancing the residual levels rather than the number of cells on each processor.